论文信息 - Expectations and entropy inequalities for finite quantum systems

Expectations and entropy inequalities for finite quantum systems

We prove that the relative entropy is decreasing under a trace-preserving expectation inB(K1), and we show the connection between this theorem and the strong subadditivity of the entropy. It is also proved that a linear, positive, trace-preserving map Φ ofB(K) into itself such that ‖Φ‖≦1 decreases the value of any convex trace function.

G. Lindblad

[1] S. Sherman,et al. Monotone and convex operator functions , 1955 .

[2] Jun Tomiyama,et al. ON THE PROJECTION OF NORM ONE IN W*-ALGEBRAS, III , 1957 .

[3] Solomon Kullback,et al. Information Theory and Statistics , 1960 .

[4] A remark on the expectations of operator algebras , 1960 .

[5] A Note on the Entropy for Operator Algebras , 1961 .

[6] H. Umegaki. Conditional expectation in an operator algebra. IV. Entropy and information , 1962 .

[7] W. Arveson. Analyticity in Operator Algebras , 1967 .

[8] Göran Lindblad,et al. An entropy inequality for quantum measurements , 1972 .

[9] E. Lieb,et al. Proof of the strong subadditivity of quantum‐mechanical entropy , 1973 .

[10] G. Lindblad. Entropy, information and quantum measurements , 1973 .

[11] E. Lieb. Convex trace functions and the Wigner-Yanase-Dyson conjecture , 1973 .